LMFDB - Embedded newform 1860.2.q.h.1141.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1860,2,Mod(1141,1860)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1860, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1860.1141"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1860.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,4,0,-4,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.8521747760$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.102293147889.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 9x^{6} + 31x^{4} - 9x^{3} + 45x^{2} + 20x + 16 $ x^8 - 2x^7 + 9x^6 + 31x^4 - 9x^3 + 45x^2 + 20x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1141.3
Root			$-0.285090 - 0.493791i$ of defining polynomial
Character	$\chi$	$=$	1860.1141
Dual form			1860.2.q.h.1741.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.28509 + 2.22584i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.07018 + 1.85361i) q^{11} +(-2.98984 + 5.17855i) q^{13} -1.00000 q^{15} +(-2.17021 - 3.75892i) q^{17} +(-1.98984 - 3.44650i) q^{19} +(-1.28509 + 2.22584i) q^{21} -7.65457 q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +0.639247 q^{29} +(5.34511 + 1.55879i) q^{31} -2.14036 q^{33} -2.57018 q^{35} +(0.285090 + 0.493791i) q^{37} -5.97967 q^{39} +(0.402947 - 0.697925i) q^{41} +(-3.60769 - 6.24871i) q^{43} +(-0.500000 - 0.866025i) q^{45} -0.229753 q^{47} +(0.197086 - 0.341363i) q^{49} +(2.17021 - 3.75892i) q^{51} +(5.76008 - 9.97676i) q^{53} +(-1.07018 - 1.85361i) q^{55} +(1.98984 - 3.44650i) q^{57} +(2.25242 + 3.90131i) q^{59} +0.358525 q^{61} -2.57018 q^{63} +(-2.98984 - 5.17855i) q^{65} +(-2.12254 + 3.67634i) q^{67} +(-3.82728 - 6.62905i) q^{69} +(-5.55534 + 9.62213i) q^{71} +(-5.50655 + 9.53762i) q^{73} +(0.500000 - 0.866025i) q^{75} -5.50111 q^{77} +(7.60221 + 13.1674i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.33027 - 9.23229i) q^{83} +4.34043 q^{85} +(0.319623 + 0.553604i) q^{87} +3.50708 q^{89} -15.3688 q^{91} +(1.32260 + 5.40839i) q^{93} +3.97967 q^{95} -8.22475 q^{97} +(-1.07018 - 1.85361i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{5} + 6 q^{7} - 4 q^{9} - q^{13} - 8 q^{15} - 7 q^{17} + 7 q^{19} - 6 q^{21} + 10 q^{23} - 4 q^{25} - 8 q^{27} - 20 q^{29} + 7 q^{31} - 12 q^{35} - 2 q^{37} - 2 q^{39} - 3 q^{41} - 4 q^{43}+ \cdots + 14 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^5 + 6 * q^7 - 4 * q^9 - q^13 - 8 * q^15 - 7 * q^17 + 7 * q^19 - 6 * q^21 + 10 * q^23 - 4 * q^25 - 8 * q^27 - 20 * q^29 + 7 * q^31 - 12 * q^35 - 2 * q^37 - 2 * q^39 - 3 * q^41 - 4 * q^43 - 4 * q^45 - 14 * q^47 + 6 * q^49 + 7 * q^51 + 11 * q^53 - 7 * q^57 + 6 * q^59 + 12 * q^61 - 12 * q^63 - q^65 + 5 * q^69 - 28 * q^71 - 13 * q^73 + 4 * q^75 - 52 * q^77 - 2 * q^79 - 4 * q^81 - q^83 + 14 * q^85 - 10 * q^87 + 20 * q^89 + 6 * q^91 - 10 * q^93 - 14 * q^95 + 14 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1860\mathbb{Z}\right)^\times$.

$n$	$931$	$1117$	$1241$	$1801$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	1.28509	+	2.22584i	0.485718	+	0.841289i	0.999865	−	0.0164131i	$-0.00522469\pi$
$7$	1.28509	+	2.22584i	0.485718	+	0.841289i	−0.514147	+	0.857702i	$0.671891\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.07018	+	1.85361i	−0.322672	+	0.558884i	−0.981038	−	0.193814i	$-0.937914\pi$
$11$	−1.07018	+	1.85361i	−0.322672	+	0.558884i	0.658367	+	0.752697i	$0.271248\pi$
$12$		0			0
$13$	−2.98984	+	5.17855i	−0.829232	+	1.43627i	0.0694101	+	0.997588i	$0.477888\pi$
$13$	−2.98984	+	5.17855i	−0.829232	+	1.43627i	−0.898642	+	0.438683i	$0.855445\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	−2.17021	−	3.75892i	−0.526354	−	0.911672i	−0.999529	−	0.0307034i	$-0.990225\pi$
$17$	−2.17021	−	3.75892i	−0.526354	−	0.911672i	0.473174	−	0.880969i	$-0.343108\pi$
$18$		0			0
$19$	−1.98984	−	3.44650i	−0.456500	−	0.790681i	0.542273	−	0.840202i	$-0.317564\pi$
$19$	−1.98984	−	3.44650i	−0.456500	−	0.790681i	−0.998773	+	0.0495211i	$0.984230\pi$
$20$		0			0
$21$	−1.28509	+	2.22584i	−0.280430	+	0.485718i
$22$		0			0
$23$	−7.65457			−1.59609			−0.798044	−	0.602599i	$-0.794132\pi$
$23$	−7.65457			−1.59609			−0.798044	+	0.602599i	$0.794132\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	0.639247			0.118705			0.0593526	−	0.998237i	$-0.481096\pi$
$29$	0.639247			0.118705			0.0593526	+	0.998237i	$0.481096\pi$
$30$		0			0
$31$	5.34511	+	1.55879i	0.960010	+	0.279967i
$31$	5.34511	+	1.55879i	0.960010	+	0.279967i
$32$		0			0
$33$	−2.14036			−0.372589
$34$		0			0
$35$	−2.57018			−0.434440
$36$		0			0
$37$	0.285090	+	0.493791i	0.0468686	+	0.0811787i	0.888508	−	0.458861i	$-0.151742\pi$
$37$	0.285090	+	0.493791i	0.0468686	+	0.0811787i	−0.841639	+	0.540040i	$0.818409\pi$
$38$		0			0
$39$	−5.97967			−0.957514
$40$		0			0
$41$	0.402947	−	0.697925i	0.0629298	−	0.108998i	−0.832844	−	0.553508i	$-0.813289\pi$
$41$	0.402947	−	0.697925i	0.0629298	−	0.108998i	0.895774	+	0.444510i	$0.146622\pi$
$42$		0			0
$43$	−3.60769	−	6.24871i	−0.550168	−	0.952919i	−0.998262	−	0.0589327i	$-0.981230\pi$
$43$	−3.60769	−	6.24871i	−0.550168	−	0.952919i	0.448094	−	0.893987i	$-0.352103\pi$
$44$		0			0
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$		0			0
$47$	−0.229753			−0.0335129			−0.0167564	−	0.999860i	$-0.505334\pi$
$47$	−0.229753			−0.0335129			−0.0167564	+	0.999860i	$0.505334\pi$
$48$		0			0
$49$	0.197086	−	0.341363i	0.0281551	−	0.0487661i
$50$		0			0
$51$	2.17021	−	3.75892i	0.303891	−	0.526354i
$52$		0			0
$53$	5.76008	−	9.97676i	0.791208	−	1.37041i	−0.134011	−	0.990980i	$-0.542786\pi$
$53$	5.76008	−	9.97676i	0.791208	−	1.37041i	0.925219	−	0.379433i	$-0.123881\pi$
$54$		0			0
$55$	−1.07018	−	1.85361i	−0.144303	−	0.249940i
$56$		0			0
$57$	1.98984	−	3.44650i	0.263560	−	0.456500i
$58$		0			0
$59$	2.25242	+	3.90131i	0.293241	+	0.507908i	0.974574	−	0.224066i	$-0.0719330\pi$
$59$	2.25242	+	3.90131i	0.293241	+	0.507908i	−0.681334	+	0.731973i	$0.738600\pi$
$60$		0			0
$61$	0.358525			0.0459044			0.0229522	−	0.999737i	$-0.492693\pi$
$61$	0.358525			0.0459044			0.0229522	+	0.999737i	$0.492693\pi$
$62$		0			0
$63$	−2.57018			−0.323812
$64$		0			0
$65$	−2.98984	−	5.17855i	−0.370844	−	0.642320i
$66$		0			0
$67$	−2.12254	+	3.67634i	−0.259309	+	0.449137i	−0.966057	−	0.258329i	$-0.916828\pi$
$67$	−2.12254	+	3.67634i	−0.259309	+	0.449137i	0.706748	+	0.707466i	$0.250162\pi$
$68$		0			0
$69$	−3.82728	−	6.62905i	−0.460751	−	0.798044i
$70$		0			0
$71$	−5.55534	+	9.62213i	−0.659297	+	1.14194i	0.321501	+	0.946909i	$0.395813\pi$
$71$	−5.55534	+	9.62213i	−0.659297	+	1.14194i	−0.980798	+	0.195027i	$0.937521\pi$
$72$		0			0
$73$	−5.50655	+	9.53762i	−0.644493	+	1.11629i	0.339926	+	0.940452i	$0.389598\pi$
$73$	−5.50655	+	9.53762i	−0.644493	+	1.11629i	−0.984418	+	0.175842i	$0.943735\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$	−5.50111			−0.626910
$78$		0			0
$79$	7.60221	+	13.1674i	0.855316	+	1.48145i	0.876352	+	0.481671i	$0.159970\pi$
$79$	7.60221	+	13.1674i	0.855316	+	1.48145i	−0.0210362	+	0.999779i	$0.506697\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	5.33027	−	9.23229i	0.585073	−	1.01338i	−0.409794	−	0.912178i	$-0.634399\pi$
$83$	5.33027	−	9.23229i	0.585073	−	1.01338i	0.994866	−	0.101197i	$-0.0322673\pi$
$84$		0			0
$85$	4.34043			0.470785
$86$		0			0
$87$	0.319623	+	0.553604i	0.0342672	+	0.0593526i
$88$		0			0
$89$	3.50708			0.371749			0.185875	−	0.982573i	$-0.440488\pi$
$89$	3.50708			0.371749			0.185875	+	0.982573i	$0.440488\pi$
$90$		0			0
$91$	−15.3688			−1.61109
$92$		0			0
$93$	1.32260	+	5.40839i	0.137148	+	0.560824i
$94$		0			0
$95$	3.97967			0.408306
$96$		0			0
$97$	−8.22475			−0.835097			−0.417548	−	0.908655i	$-0.637111\pi$
$97$	−8.22475			−0.835097			−0.417548	+	0.908655i	$0.637111\pi$
$98$		0			0
$99$	−1.07018	−	1.85361i	−0.107557	−	0.186295i
$100$		0			0
$101$	−17.8793			−1.77906			−0.889529	−	0.456878i	$-0.848968\pi$
$101$	−17.8793			−1.77906			−0.889529	+	0.456878i	$0.848968\pi$
$102$		0			0
$103$	−4.61349	+	7.99080i	−0.454581	+	0.787357i	−0.998664	−	0.0516745i	$-0.983544\pi$
$103$	−4.61349	+	7.99080i	−0.454581	+	0.787357i	0.544083	+	0.839031i	$0.316878\pi$
$104$		0			0
$105$	−1.28509	−	2.22584i	−0.125412	−	0.217220i
$106$		0			0
$107$	−8.70804	−	15.0828i	−0.841838	−	1.45811i	−0.888339	−	0.459188i	$-0.848140\pi$
$107$	−8.70804	−	15.0828i	−0.841838	−	1.45811i	0.0465012	−	0.998918i	$-0.485193\pi$
$108$		0			0
$109$	−1.82399			−0.174707			−0.0873534	−	0.996177i	$-0.527841\pi$
$109$	−1.82399			−0.174707			−0.0873534	+	0.996177i	$0.527841\pi$
$110$		0			0
$111$	−0.285090	+	0.493791i	−0.0270596	+	0.0468686i
$112$		0			0
$113$	−5.37608	+	9.31164i	−0.505739	+	0.875965i	0.494239	+	0.869326i	$0.335447\pi$
$113$	−5.37608	+	9.31164i	−0.505739	+	0.875965i	−0.999978	+	0.00663911i	$0.997887\pi$
$114$		0			0
$115$	3.82728	−	6.62905i	0.356896	−	0.618162i
$116$		0			0
$117$	−2.98984	−	5.17855i	−0.276411	−	0.478757i
$118$		0			0
$119$	5.57784	−	9.66110i	0.511320	−	0.885632i
$120$		0			0
$121$	3.20943	+	5.55889i	0.291766	+	0.505354i
$122$		0			0
$123$	0.805895			0.0726651
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	11.1677	+	19.3430i	0.990974	+	1.71642i	0.611580	+	0.791182i	$0.290534\pi$
$127$	11.1677	+	19.3430i	0.990974	+	1.71642i	0.379394	+	0.925235i	$0.376132\pi$
$128$		0			0
$129$	3.60769	−	6.24871i	0.317640	−	0.550168i
$130$		0			0
$131$	3.75524	+	6.50426i	0.328097	+	0.568280i	0.982134	−	0.188182i	$-0.0602595\pi$
$131$	3.75524	+	6.50426i	0.328097	+	0.568280i	−0.654038	+	0.756462i	$0.726926\pi$
$132$		0			0
$133$	5.11424	−	8.85813i	0.443461	−	0.768097i
$134$		0			0
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$		0			0
$137$	5.74226	−	9.94589i	0.490594	−	0.849735i	−0.509347	−	0.860561i	$-0.670113\pi$
$137$	5.74226	−	9.94589i	0.490594	−	0.849735i	0.999941	+	0.0108268i	$0.00344633\pi$
$138$		0			0
$139$	1.20943			0.102582			0.0512911	−	0.998684i	$-0.483666\pi$
$139$	1.20943			0.102582			0.0512911	+	0.998684i	$0.483666\pi$
$140$		0			0
$141$	−0.114876	−	0.198972i	−0.00967434	−	0.0167564i
$142$		0			0
$143$	−6.39933	−	11.0840i	−0.535139	−	0.926888i
$144$		0			0
$145$	−0.319623	+	0.553604i	−0.0265433	+	0.0459743i
$146$		0			0
$147$	0.394172			0.0325108
$148$		0			0
$149$	2.50187	+	4.33336i	0.204961	+	0.355003i	0.950120	−	0.311884i	$-0.100960\pi$
$149$	2.50187	+	4.33336i	0.204961	+	0.355003i	−0.745159	+	0.666886i	$0.767627\pi$
$150$		0			0
$151$	−1.06567			−0.0867228			−0.0433614	−	0.999059i	$-0.513807\pi$
$151$	−1.06567			−0.0867228			−0.0433614	+	0.999059i	$0.513807\pi$
$152$		0			0
$153$	4.34043			0.350903
$154$		0			0
$155$	−4.02250	+	3.84961i	−0.323095	+	0.309208i
$156$		0			0
$157$	−22.5842			−1.80242			−0.901209	−	0.433385i	$-0.857319\pi$
$157$	−22.5842			−1.80242			−0.901209	+	0.433385i	$0.857319\pi$
$158$		0			0
$159$	11.5202			0.913609
$160$		0			0
$161$	−9.83681	−	17.0379i	−0.775249	−	1.34277i
$162$		0			0
$163$	−14.7318			−1.15389			−0.576943	−	0.816785i	$-0.695754\pi$
$163$	−14.7318			−1.15389			−0.576943	+	0.816785i	$0.695754\pi$
$164$		0			0
$165$	1.07018	−	1.85361i	0.0833134	−	0.144303i
$166$		0			0
$167$	0.560018	+	0.969979i	0.0433355	+	0.0750592i	0.886880	−	0.462001i	$-0.152868\pi$
$167$	0.560018	+	0.969979i	0.0433355	+	0.0750592i	−0.843544	+	0.537060i	$0.819535\pi$
$168$		0			0
$169$	−11.3783	−	19.7077i	−0.875250	−	1.51598i
$170$		0			0
$171$	3.97967			0.304333
$172$		0			0
$173$	−5.65128	+	9.78830i	−0.429659	+	0.744190i	−0.996843	−	0.0794005i	$-0.974699\pi$
$173$	−5.65128	+	9.78830i	−0.429659	+	0.744190i	0.567184	+	0.823591i	$0.308033\pi$
$174$		0			0
$175$	1.28509	−	2.22584i	0.0971437	−	0.168258i
$176$		0			0
$177$	−2.25242	+	3.90131i	−0.169303	+	0.293241i
$178$		0			0
$179$	3.25572	+	5.63907i	0.243344	+	0.421484i	0.961665	−	0.274228i	$-0.0884224\pi$
$179$	3.25572	+	5.63907i	0.243344	+	0.421484i	−0.718321	+	0.695712i	$0.755089\pi$
$180$		0			0
$181$	2.57784	−	4.46495i	0.191609	−	0.331877i	−0.754174	−	0.656674i	$-0.771963\pi$
$181$	2.57784	−	4.46495i	0.191609	−	0.331877i	0.945784	+	0.324797i	$0.105296\pi$
$182$		0			0
$183$	0.179262	+	0.310491i	0.0132515	+	0.0229522i
$184$		0			0
$185$	−0.570181			−0.0419205
$186$		0			0
$187$	9.29008			0.679358
$188$		0			0
$189$	−1.28509	−	2.22584i	−0.0934766	−	0.161906i
$190$		0			0
$191$	−7.22007	+	12.5055i	−0.522426	+	0.904868i	0.477234	+	0.878776i	$0.341640\pi$
$191$	−7.22007	+	12.5055i	−0.522426	+	0.904868i	−0.999660	+	0.0260917i	$0.991694\pi$
$192$		0			0
$193$	9.75822	+	16.9017i	0.702412	+	1.21661i	0.967617	+	0.252421i	$0.0812269\pi$
$193$	9.75822	+	16.9017i	0.702412	+	1.21661i	−0.265206	+	0.964192i	$0.585440\pi$
$194$		0			0
$195$	2.98984	−	5.17855i	0.214107	−	0.370844i
$196$		0			0
$197$	−7.11237	+	12.3190i	−0.506736	+	0.877692i	0.493234	+	0.869897i	$0.335815\pi$
$197$	−7.11237	+	12.3190i	−0.506736	+	0.877692i	−0.999970	+	0.00779527i	$0.997519\pi$
$198$		0			0
$199$	9.67489	−	16.7574i	0.685835	−	1.18790i	−0.287339	−	0.957829i	$-0.592770\pi$
$199$	9.67489	−	16.7574i	0.685835	−	1.18790i	0.973174	−	0.230072i	$-0.0738962\pi$
$200$		0			0
$201$	−4.24507			−0.299424
$202$		0			0
$203$	0.821490	+	1.42286i	0.0576573	+	0.0998653i
$204$		0			0
$205$	0.402947	+	0.697925i	0.0281431	+	0.0487452i
$206$		0			0
$207$	3.82728	−	6.62905i	0.266015	−	0.460751i
$208$		0			0
$209$	8.51794			0.589198
$210$		0			0
$211$	10.9229	+	18.9191i	0.751967	+	1.30244i	0.946868	+	0.321622i	$0.104228\pi$
$211$	10.9229	+	18.9191i	0.751967	+	1.30244i	−0.194901	+	0.980823i	$0.562439\pi$
$212$		0			0
$213$	−11.1107			−0.761291
$214$		0			0
$215$	7.21539			0.492085
$216$		0			0
$217$	3.39933	+	13.9005i	0.230762	+	0.943631i
$218$		0			0
$219$	−11.0131			−0.744196
$220$		0			0
$221$	25.9543			1.74588
$222$		0			0
$223$	11.7669	+	20.3809i	0.787973	+	1.36481i	0.927207	+	0.374549i	$0.122203\pi$
$223$	11.7669	+	20.3809i	0.787973	+	1.36481i	−0.139234	+	0.990259i	$0.544464\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	9.04517	−	15.6667i	0.600349	−	1.03984i	−0.392419	−	0.919787i	$-0.628362\pi$
$227$	9.04517	−	15.6667i	0.600349	−	1.03984i	0.992768	−	0.120049i	$-0.0383051\pi$
$228$		0			0
$229$	−4.70943	−	8.15697i	−0.311208	−	0.539028i	0.667416	−	0.744685i	$-0.267400\pi$
$229$	−4.70943	−	8.15697i	−0.311208	−	0.539028i	−0.978624	+	0.205657i	$0.934067\pi$
$230$		0			0
$231$	−2.75056	−	4.76410i	−0.180973	−	0.313455i
$232$		0			0
$233$	−27.7159			−1.81573			−0.907863	−	0.419267i	$-0.862287\pi$
$233$	−27.7159			−1.81573			−0.907863	+	0.419267i	$0.862287\pi$
$234$		0			0
$235$	0.114876	−	0.198972i	0.00749371	−	0.0129795i
$236$		0			0
$237$	−7.60221	+	13.1674i	−0.493817	+	0.855316i
$238$		0			0
$239$	7.27774	−	12.6054i	0.470758	−	0.815377i	−0.528683	−	0.848820i	$-0.677314\pi$
$239$	7.27774	−	12.6054i	0.470758	−	0.815377i	0.999441	+	0.0334429i	$0.0106472\pi$
$240$		0			0
$241$	6.30807	+	10.9259i	0.406339	+	0.703799i	0.994476	−	0.104962i	$-0.0334720\pi$
$241$	6.30807	+	10.9259i	0.406339	+	0.703799i	−0.588138	+	0.808761i	$0.700139\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	0.197086	+	0.341363i	0.0125914	+	0.0218089i
$246$		0			0
$247$	23.7972			1.51418
$248$		0			0
$249$	10.6605			0.675584
$250$		0			0
$251$	5.11488	+	8.85923i	0.322848	+	0.559189i	0.981074	−	0.193631i	$-0.0620264\pi$
$251$	5.11488	+	8.85923i	0.322848	+	0.559189i	−0.658226	+	0.752820i	$0.728693\pi$
$252$		0			0
$253$	8.19177	−	14.1886i	0.515012	−	0.892027i
$254$		0			0
$255$	2.17021	+	3.75892i	0.135904	+	0.235393i
$256$		0			0
$257$	−11.6938	+	20.2542i	−0.729438	+	1.26342i	0.227683	+	0.973735i	$0.426885\pi$
$257$	−11.6938	+	20.2542i	−0.729438	+	1.26342i	−0.957121	+	0.289688i	$0.906448\pi$
$258$		0			0
$259$	−0.732733	+	1.26913i	−0.0455298	+	0.0788600i
$260$		0			0
$261$	−0.319623	+	0.553604i	−0.0197842	+	0.0342672i
$262$		0			0
$263$	13.8793			0.855835			0.427918	−	0.903818i	$-0.359247\pi$
$263$	13.8793			0.855835			0.427918	+	0.903818i	$0.359247\pi$
$264$		0			0
$265$	5.76008	+	9.97676i	0.353839	+	0.612867i
$266$		0			0
$267$	1.75354	+	3.03722i	0.107315	+	0.185875i
$268$		0			0
$269$	1.13925	−	1.97323i	0.0694611	−	0.120310i	−0.829203	−	0.558947i	$-0.811205\pi$
$269$	1.13925	−	1.97323i	0.0694611	−	0.120310i	0.898664	+	0.438637i	$0.144539\pi$
$270$		0			0
$271$	−0.135358			−0.00822239			−0.00411119	−	0.999992i	$-0.501309\pi$
$271$	−0.135358			−0.00822239			−0.00411119	+	0.999992i	$0.501309\pi$
$272$		0			0
$273$	−7.68442	−	13.3098i	−0.465082	−	0.805546i
$274$		0			0
$275$	2.14036			0.129069
$276$		0			0
$277$	6.39980			0.384527			0.192263	−	0.981343i	$-0.438417\pi$
$277$	6.39980			0.384527			0.192263	+	0.981343i	$0.438417\pi$
$278$		0			0
$279$	−4.02250	+	3.84961i	−0.240821	+	0.230470i
$280$		0			0
$281$	−11.6568			−0.695386			−0.347693	−	0.937608i	$-0.613035\pi$
$281$	−11.6568			−0.695386			−0.347693	+	0.937608i	$0.613035\pi$
$282$		0			0
$283$	−12.6489			−0.751901			−0.375951	−	0.926640i	$-0.622684\pi$
$283$	−12.6489			−0.751901			−0.375951	+	0.926640i	$0.622684\pi$
$284$		0			0
$285$	1.98984	+	3.44650i	0.117868	+	0.204153i
$286$		0			0
$287$	2.07129			0.122265
$288$		0			0
$289$	−0.919657	+	1.59289i	−0.0540975	+	0.0936995i
$290$		0			0
$291$	−4.11237	−	7.12284i	−0.241072	−	0.417548i
$292$		0			0
$293$	0.890918	+	1.54312i	0.0520480	+	0.0901498i	0.890876	−	0.454247i	$-0.150092\pi$
$293$	0.890918	+	1.54312i	0.0520480	+	0.0901498i	−0.838828	+	0.544397i	$0.816758\pi$
$294$		0			0
$295$	−4.50485			−0.262282
$296$		0			0
$297$	1.07018	−	1.85361i	0.0620982	−	0.107557i
$298$		0			0
$299$	22.8859	−	39.6396i	1.32353	−	2.29242i
$300$		0			0
$301$	9.27243	−	16.0603i	0.534454	−	0.925701i
$302$		0			0
$303$	−8.93966	−	15.4839i	−0.513570	−	0.889529i
$304$		0			0
$305$	−0.179262	+	0.310491i	−0.0102645	+	0.0177787i
$306$		0			0
$307$	7.91061	+	13.7016i	0.451482	+	0.781990i	0.998478	−	0.0551449i	$-0.0175621\pi$
$307$	7.91061	+	13.7016i	0.451482	+	0.781990i	−0.546996	+	0.837135i	$0.684229\pi$
$308$		0			0
$309$	−9.22698			−0.524904
$310$		0			0
$311$	−9.01905			−0.511424			−0.255712	−	0.966753i	$-0.582310\pi$
$311$	−9.01905			−0.511424			−0.255712	+	0.966753i	$0.582310\pi$
$312$		0			0
$313$	0.146429	+	0.253622i	0.00827664	+	0.0143356i	0.870134	−	0.492815i	$-0.164032\pi$
$313$	0.146429	+	0.253622i	0.00827664	+	0.0143356i	−0.861857	+	0.507151i	$0.830699\pi$
$314$		0			0
$315$	1.28509	−	2.22584i	0.0724066	−	0.125412i
$316$		0			0
$317$	−5.61722	−	9.72931i	−0.315495	−	0.546453i	0.664048	−	0.747690i	$-0.268837\pi$
$317$	−5.61722	−	9.72931i	−0.315495	−	0.546453i	−0.979543	+	0.201237i	$0.935504\pi$
$318$		0			0
$319$	−0.684109	+	1.18491i	−0.0383028	+	0.0663423i
$320$		0			0
$321$	8.70804	−	15.0828i	0.486035	−	0.841838i
$322$		0			0
$323$	−8.63674	+	14.9593i	−0.480561	+	0.832357i
$324$		0			0
$325$	5.97967			0.331693
$326$		0			0
$327$	−0.911996	−	1.57962i	−0.0504335	−	0.0873534i
$328$		0			0
$329$	−0.295253	−	0.511393i	−0.0162778	−	0.0281940i
$330$		0			0
$331$	−16.5878	+	28.7310i	−0.911751	+	1.57920i	−0.100160	+	0.994971i	$0.531936\pi$
$331$	−16.5878	+	28.7310i	−0.911751	+	1.57920i	−0.811590	+	0.584227i	$0.801398\pi$
$332$		0			0
$333$	−0.570181			−0.0312457
$334$		0			0
$335$	−2.12254	−	3.67634i	−0.115967	−	0.200860i
$336$		0			0
$337$	−1.70714			−0.0929940			−0.0464970	−	0.998918i	$-0.514806\pi$
$337$	−1.70714			−0.0929940			−0.0464970	+	0.998918i	$0.514806\pi$
$338$		0			0
$339$	−10.7522			−0.583977
$340$		0			0
$341$	−8.60961	+	8.23955i	−0.466237	+	0.446196i
$342$		0			0
$343$	19.0044			1.02614
$344$		0			0
$345$	7.65457			0.412108
$346$		0			0
$347$	2.35246	+	4.07457i	0.126287	+	0.218735i	0.922235	−	0.386630i	$-0.126361\pi$
$347$	2.35246	+	4.07457i	0.126287	+	0.218735i	−0.795949	+	0.605364i	$0.793027\pi$
$348$		0			0
$349$	11.9603			0.640221			0.320110	−	0.947380i	$-0.396280\pi$
$349$	11.9603			0.640221			0.320110	+	0.947380i	$0.396280\pi$
$350$		0			0
$351$	2.98984	−	5.17855i	0.159586	−	0.276411i
$352$		0			0
$353$	7.60689	+	13.1755i	0.404874	+	0.701262i	0.994307	−	0.106555i	$-0.0339820\pi$
$353$	7.60689	+	13.1755i	0.404874	+	0.701262i	−0.589433	+	0.807817i	$0.700649\pi$
$354$		0			0
$355$	−5.55534	−	9.62213i	−0.294847	−	0.510689i
$356$		0			0
$357$	11.1557			0.590421
$358$		0			0
$359$	14.5145	−	25.1399i	0.766047	−	1.32683i	−0.173644	−	0.984808i	$-0.555554\pi$
$359$	14.5145	−	25.1399i	0.766047	−	1.32683i	0.939691	−	0.342024i	$-0.111112\pi$
$360$		0			0
$361$	1.58110	−	2.73854i	0.0832155	−	0.144134i
$362$		0			0
$363$	−3.20943	+	5.55889i	−0.168451	+	0.291766i
$364$		0			0
$365$	−5.50655	−	9.53762i	−0.288226	−	0.499222i
$366$		0			0
$367$	3.34463	−	5.79307i	0.174588	−	0.302396i	−0.765430	−	0.643519i	$-0.777474\pi$
$367$	3.34463	−	5.79307i	0.174588	−	0.302396i	0.940019	+	0.341123i	$0.110807\pi$
$368$		0			0
$369$	0.402947	+	0.697925i	0.0209766	+	0.0363325i
$370$		0			0
$371$	29.6089			1.53722
$372$		0			0
$373$	−11.4982			−0.595356			−0.297678	−	0.954666i	$-0.596212\pi$
$373$	−11.4982			−0.595356			−0.297678	+	0.954666i	$0.596212\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	−1.91124	+	3.31037i	−0.0984341	+	0.170493i
$378$		0			0
$379$	14.3659	+	24.8825i	0.737927	+	1.27813i	0.953427	+	0.301624i	$0.0975286\pi$
$379$	14.3659	+	24.8825i	0.737927	+	1.27813i	−0.215500	+	0.976504i	$0.569138\pi$
$380$		0			0
$381$	−11.1677	+	19.3430i	−0.572139	+	0.990974i
$382$		0			0
$383$	2.57375	−	4.45786i	0.131512	−	0.227786i	−0.792747	−	0.609550i	$-0.791350\pi$
$383$	2.57375	−	4.45786i	0.131512	−	0.227786i	0.924260	+	0.381764i	$0.124683\pi$
$384$		0			0
$385$	2.75056	−	4.76410i	0.140181	−	0.242801i
$386$		0			0
$387$	7.21539			0.366779
$388$		0			0
$389$	−18.2014	−	31.5258i	−0.922850	−	1.59842i	−0.794983	−	0.606631i	$-0.792520\pi$
$389$	−18.2014	−	31.5258i	−0.922850	−	1.59842i	−0.127867	−	0.991791i	$-0.540813\pi$
$390$		0			0
$391$	16.6121	+	28.7729i	0.840108	+	1.45511i
$392$		0			0
$393$	−3.75524	+	6.50426i	−0.189427	+	0.328097i
$394$		0			0
$395$	−15.2044			−0.765018
$396$		0			0
$397$	10.1696	+	17.6142i	0.510397	+	0.884033i	0.999927	+	0.0120468i	$0.00383469\pi$
$397$	10.1696	+	17.6142i	0.510397	+	0.884033i	−0.489531	+	0.871986i	$0.662832\pi$
$398$		0			0
$399$	10.2285			0.512065
$400$		0			0
$401$	8.32733			0.415847			0.207924	−	0.978145i	$-0.433329\pi$
$401$	8.32733			0.415847			0.207924	+	0.978145i	$0.433329\pi$
$402$		0			0
$403$	−24.0533	+	23.0194i	−1.19818	+	1.14668i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−1.22039			−0.0604926
$408$		0			0
$409$	2.90401	+	5.02990i	0.143594	+	0.248712i	0.928848	−	0.370462i	$-0.120801\pi$
$409$	2.90401	+	5.02990i	0.143594	+	0.248712i	−0.785253	+	0.619174i	$0.787467\pi$
$410$		0			0
$411$	11.4845			0.566490
$412$		0			0
$413$	−5.78914	+	10.0271i	−0.284865	+	0.493400i
$414$		0			0
$415$	5.33027	+	9.23229i	0.261652	+	0.453195i
$416$		0			0
$417$	0.604714	+	1.04739i	0.0296130	+	0.0512911i
$418$		0			0
$419$	27.0410			1.32104			0.660519	−	0.750810i	$-0.270336\pi$
$419$	27.0410			1.32104			0.660519	+	0.750810i	$0.270336\pi$
$420$		0			0
$421$	0.114291	−	0.197958i	0.00557021	−	0.00964789i	−0.863227	−	0.504816i	$-0.831560\pi$
$421$	0.114291	−	0.197958i	0.00557021	−	0.00964789i	0.868797	+	0.495168i	$0.164894\pi$
$422$		0			0
$423$	0.114876	−	0.198972i	0.00558548	−	0.00967434i
$424$		0			0
$425$	−2.17021	+	3.75892i	−0.105271	+	0.182334i
$426$		0			0
$427$	0.460736	+	0.798019i	0.0222966	+	0.0386188i
$428$		0			0
$429$	6.39933	−	11.0840i	0.308963	−	0.535139i
$430$		0			0
$431$	7.54768	+	13.0730i	0.363559	+	0.629702i	0.988544	−	0.150934i	$-0.0482283\pi$
$431$	7.54768	+	13.0730i	0.363559	+	0.629702i	−0.624985	+	0.780637i	$0.714895\pi$
$432$		0			0
$433$	−29.6686			−1.42578			−0.712891	−	0.701274i	$-0.752615\pi$
$433$	−29.6686			−1.42578			−0.712891	+	0.701274i	$0.752615\pi$
$434$		0			0
$435$	−0.639247			−0.0306495
$436$		0			0
$437$	15.2313	+	26.3815i	0.728614	+	1.26200i
$438$		0			0
$439$	1.85399	−	3.21120i	0.0884861	−	0.153262i	−0.818385	−	0.574670i	$-0.805130\pi$
$439$	1.85399	−	3.21120i	0.0884861	−	0.153262i	0.906871	+	0.421407i	$0.138464\pi$
$440$		0			0
$441$	0.197086	+	0.341363i	0.00938505	+	0.0162554i
$442$		0			0
$443$	−9.54549	+	16.5333i	−0.453520	+	0.785519i	−0.998602	−	0.0528635i	$-0.983165\pi$
$443$	−9.54549	+	16.5333i	−0.453520	+	0.785519i	0.545082	+	0.838383i	$0.316499\pi$
$444$		0			0
$445$	−1.75354	+	3.03722i	−0.0831257	+	0.143978i
$446$		0			0
$447$	−2.50187	+	4.33336i	−0.118334	+	0.204961i
$448$		0			0
$449$	3.96721			0.187224			0.0936120	−	0.995609i	$-0.470159\pi$
$449$	3.96721			0.187224			0.0936120	+	0.995609i	$0.470159\pi$
$450$		0			0
$451$	0.862453	+	1.49381i	0.0406113	+	0.0703409i
$452$		0			0
$453$	−0.532834	−	0.922895i	−0.0250347	−	0.0433614i
$454$		0			0
$455$	7.68442	−	13.3098i	0.360251	−	0.623973i
$456$		0			0
$457$	27.2088			1.27277			0.636387	−	0.771370i	$-0.280428\pi$
$457$	27.2088			1.27277			0.636387	+	0.771370i	$0.280428\pi$
$458$		0			0
$459$	2.17021	+	3.75892i	0.101297	+	0.175451i
$460$		0			0
$461$	−14.8974			−0.693842			−0.346921	−	0.937894i	$-0.612773\pi$
$461$	−14.8974			−0.693842			−0.346921	+	0.937894i	$0.612773\pi$
$462$		0			0
$463$	29.4042			1.36653			0.683264	−	0.730172i	$-0.260560\pi$
$463$	29.4042			1.36653			0.683264	+	0.730172i	$0.260560\pi$
$464$		0			0
$465$	−5.34511	−	1.55879i	−0.247873	−	0.0722871i
$466$		0			0
$467$	−31.3717			−1.45171			−0.725854	−	0.687848i	$-0.758555\pi$
$467$	−31.3717			−1.45171			−0.725854	+	0.687848i	$0.758555\pi$
$468$		0			0
$469$	−10.9106			−0.503805
$470$		0			0
$471$	−11.2921	−	19.5585i	−0.520313	−	0.901209i
$472$		0			0
$473$	15.4435			0.710095
$474$		0			0
$475$	−1.98984	+	3.44650i	−0.0913000	+	0.158136i
$476$		0			0
$477$	5.76008	+	9.97676i	0.263736	+	0.456804i
$478$		0			0
$479$	13.3981	+	23.2062i	0.612175	+	1.06032i	0.990873	+	0.134798i	$0.0430387\pi$
$479$	13.3981	+	23.2062i	0.612175	+	1.06032i	−0.378698	+	0.925520i	$0.623628\pi$
$480$		0			0
$481$	−3.40949			−0.155460
$482$		0			0
$483$	9.83681	−	17.0379i	0.447590	−	0.775249i
$484$		0			0
$485$	4.11237	−	7.12284i	0.186733	−	0.323432i
$486$		0			0
$487$	12.4433	−	21.5524i	0.563859	−	0.976632i	−0.433296	−	0.901252i	$-0.642650\pi$
$487$	12.4433	−	21.5524i	0.563859	−	0.976632i	0.997155	−	0.0753802i	$-0.0240170\pi$
$488$		0			0
$489$	−7.36591	−	12.7581i	−0.333098	−	0.576943i
$490$		0			0
$491$	15.5863	−	26.9962i	0.703398	−	1.21832i	−0.263869	−	0.964559i	$-0.584999\pi$
$491$	15.5863	−	26.9962i	0.703398	−	1.21832i	0.967267	−	0.253762i	$-0.0816681\pi$
$492$		0			0
$493$	−1.38730	−	2.40288i	−0.0624809	−	0.108220i
$494$		0			0
$495$	2.14036			0.0962021
$496$		0			0
$497$	−28.5564			−1.28093
$498$		0			0
$499$	1.96733	+	3.40752i	0.0880699	+	0.152542i	0.906695	−	0.421786i	$-0.138597\pi$
$499$	1.96733	+	3.40752i	0.0880699	+	0.152542i	−0.818625	+	0.574328i	$0.805263\pi$
$500$		0			0
$501$	−0.560018	+	0.969979i	−0.0250197	+	0.0433355i
$502$		0			0
$503$	16.2749	+	28.1890i	0.725663	+	1.25689i	0.958700	+	0.284418i	$0.0918002\pi$
$503$	16.2749	+	28.1890i	0.725663	+	1.25689i	−0.233037	+	0.972468i	$0.574866\pi$
$504$		0			0
$505$	8.93966	−	15.4839i	0.397810	−	0.689026i
$506$		0			0
$507$	11.3783	−	19.7077i	0.505326	−	0.875250i
$508$		0			0
$509$	4.64019	−	8.03705i	0.205673	−	0.356236i	−0.744674	−	0.667428i	$-0.767395\pi$
$509$	4.64019	−	8.03705i	0.205673	−	0.356236i	0.950347	+	0.311192i	$0.100728\pi$
$510$		0			0
$511$	−28.3056			−1.25217
$512$		0			0
$513$	1.98984	+	3.44650i	0.0878535	+	0.152167i
$514$		0			0
$515$	−4.61349	−	7.99080i	−0.203295	−	0.352117i
$516$		0			0
$517$	0.245877	−	0.425871i	0.0108137	−	0.0187298i
$518$		0			0
$519$	−11.3026			−0.496127
$520$		0			0
$521$	−13.2236	−	22.9040i	−0.579338	−	1.00344i	−0.995555	−	0.0941777i	$-0.969978\pi$
$521$	−13.2236	−	22.9040i	−0.579338	−	1.00344i	0.416217	−	0.909265i	$-0.363356\pi$
$522$		0			0
$523$	38.6231			1.68887			0.844434	−	0.535659i	$-0.179937\pi$
$523$	38.6231			1.68887			0.844434	+	0.535659i	$0.179937\pi$
$524$		0			0
$525$	2.57018			0.112172
$526$		0			0
$527$	−5.74067	−	23.4747i	−0.250067	−	1.02258i
$528$		0			0
$529$	35.5924			1.54750
$530$		0			0
$531$	−4.50485			−0.195494
$532$		0			0
$533$	2.40949	+	4.17337i	0.104367	+	0.180769i
$534$		0			0
$535$	17.4161			0.752963
$536$		0			0
$537$	−3.25572	+	5.63907i	−0.140495	+	0.243344i
$538$		0			0
$539$	0.421835	+	0.730640i	0.0181697	+	0.0314709i
$540$		0			0
$541$	1.39465	+	2.41561i	0.0599607	+	0.103855i	0.894448	−	0.447173i	$-0.147569\pi$
$541$	1.39465	+	2.41561i	0.0599607	+	0.103855i	−0.834487	+	0.551028i	$0.814236\pi$
$542$		0			0
$543$	5.15568			0.221252
$544$		0			0
$545$	0.911996	−	1.57962i	0.0390656	−	0.0676636i
$546$		0			0
$547$	8.86836	−	15.3605i	0.379184	−	0.656766i	−0.611760	−	0.791044i	$-0.709538\pi$
$547$	8.86836	−	15.3605i	0.379184	−	0.656766i	0.990944	+	0.134278i	$0.0428715\pi$
$548$		0			0
$549$	−0.179262	+	0.310491i	−0.00765073	+	0.0132515i
$550$		0			0
$551$	−1.27200	−	2.20316i	−0.0541889	−	0.0938579i
$552$		0			0
$553$	−19.5391	+	33.8426i	−0.830885	+	1.43914i
$554$		0			0
$555$	−0.285090	−	0.493791i	−0.0121014	−	0.0209603i
$556$		0			0
$557$	0.0290618			0.00123139			0.000615693	−	1.00000i	$-0.499804\pi$
$557$	0.0290618			0.00123139			0.000615693		1.00000i	$0.499804\pi$
$558$		0			0
$559$	43.1457			1.82487
$560$		0			0
$561$	4.64504	+	8.04545i	0.196114	+	0.339679i
$562$		0			0
$563$	−12.1772	+	21.0916i	−0.513209	+	0.888905i	0.486673	+	0.873584i	$0.338210\pi$
$563$	−12.1772	+	21.0916i	−0.513209	+	0.888905i	−0.999883	+	0.0153207i	$0.995123\pi$
$564$		0			0
$565$	−5.37608	−	9.31164i	−0.226173	−	0.391743i
$566$		0			0
$567$	1.28509	−	2.22584i	0.0539687	−	0.0934766i
$568$		0			0
$569$	−2.10769	+	3.65063i	−0.0883591	+	0.153043i	−0.906818	−	0.421523i	$-0.861496\pi$
$569$	−2.10769	+	3.65063i	−0.0883591	+	0.153043i	0.818459	+	0.574566i	$0.194829\pi$
$570$		0			0
$571$	12.9106	−	22.3617i	0.540290	−	0.935810i	−0.458597	−	0.888644i	$-0.651648\pi$
$571$	12.9106	−	22.3617i	0.540290	−	0.935810i	0.998887	−	0.0471655i	$-0.0150188\pi$
$572$		0			0
$573$	−14.4401			−0.603245
$574$		0			0
$575$	3.82728	+	6.62905i	0.159609	+	0.276451i
$576$		0			0
$577$	−19.7976	−	34.2904i	−0.824185	−	1.42753i	−0.902541	−	0.430605i	$-0.858300\pi$
$577$	−19.7976	−	34.2904i	−0.824185	−	1.42753i	0.0783559	−	0.996925i	$-0.475033\pi$
$578$		0			0
$579$	−9.75822	+	16.9017i	−0.405538	+	0.702412i
$580$		0			0
$581$	27.3995			1.13672
$582$		0			0
$583$	12.3287	+	21.3539i	0.510601	+	0.884387i
$584$		0			0
$585$	5.97967			0.247229
$586$		0			0
$587$	0.895620			0.0369662			0.0184831	−	0.999829i	$-0.494116\pi$
$587$	0.895620			0.0369662			0.0184831	+	0.999829i	$0.494116\pi$
$588$		0			0
$589$	−5.26353	−	21.5236i	−0.216880	−	0.886866i
$590$		0			0
$591$	−14.2247			−0.585128
$592$		0			0
$593$	44.1638			1.81359			0.906794	−	0.421573i	$-0.138522\pi$
$593$	44.1638			1.81359			0.906794	+	0.421573i	$0.138522\pi$
$594$		0			0
$595$	5.57784	+	9.66110i	0.228669	+	0.396067i
$596$		0			0
$597$	19.3498			0.791934
$598$		0			0
$599$	21.2454	−	36.7981i	0.868063	−	1.50353i	0.00408962	−	0.999992i	$-0.498698\pi$
$599$	21.2454	−	36.7981i	0.868063	−	1.50353i	0.863973	−	0.503538i	$-0.167968\pi$
$600$		0			0
$601$	−19.6150	−	33.9742i	−0.800114	−	1.38584i	−0.919541	−	0.392995i	$-0.871439\pi$
$601$	−19.6150	−	33.9742i	−0.800114	−	1.38584i	0.119427	−	0.992843i	$-0.461894\pi$
$602$		0			0
$603$	−2.12254	−	3.67634i	−0.0864364	−	0.149712i
$604$		0			0
$605$	−6.41885			−0.260964
$606$		0			0
$607$	−6.31074	+	10.9305i	−0.256145	+	0.443656i	−0.965206	−	0.261491i	$-0.915786\pi$
$607$	−6.31074	+	10.9305i	−0.256145	+	0.443656i	0.709061	+	0.705147i	$0.249119\pi$
$608$		0			0
$609$	−0.821490	+	1.42286i	−0.0332884	+	0.0576573i
$610$		0			0
$611$	0.686923	−	1.18979i	0.0277899	−	0.0481336i
$612$		0			0
$613$	−22.5907	−	39.1282i	−0.912428	−	1.58037i	−0.810624	−	0.585568i	$-0.800872\pi$
$613$	−22.5907	−	39.1282i	−0.912428	−	1.58037i	−0.101805	−	0.994804i	$-0.532462\pi$
$614$		0			0
$615$	−0.402947	+	0.697925i	−0.0162484	+	0.0281431i
$616$		0			0
$617$	−5.24853	−	9.09073i	−0.211298	−	0.365979i	0.740823	−	0.671700i	$-0.234436\pi$
$617$	−5.24853	−	9.09073i	−0.211298	−	0.365979i	−0.952121	+	0.305721i	$0.901102\pi$
$618$		0			0
$619$	18.7383			0.753157			0.376579	−	0.926385i	$-0.377100\pi$
$619$	18.7383			0.753157			0.376579	+	0.926385i	$0.377100\pi$
$620$		0			0
$621$	7.65457			0.307167
$622$		0			0
$623$	4.50691	+	7.80620i	0.180565	+	0.312749i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	4.25897	+	7.37675i	0.170087	+	0.294599i
$628$		0			0
$629$	1.23741	−	2.14326i	0.0493389	−	0.0854575i
$630$		0			0
$631$	−2.74758	+	4.75894i	−0.109379	+	0.189450i	−0.915519	−	0.402275i	$-0.868220\pi$
$631$	−2.74758	+	4.75894i	−0.109379	+	0.189450i	0.806140	+	0.591725i	$0.201553\pi$
$632$		0			0
$633$	−10.9229	+	18.9191i	−0.434148	+	0.751967i
$634$		0			0
$635$	−22.3354			−0.886354
$636$		0			0
$637$	1.17851	+	2.04124i	0.0466943	+	0.0808769i
$638$		0			0
$639$	−5.55534	−	9.62213i	−0.219766	−	0.380645i
$640$		0			0
$641$	−9.22332	+	15.9753i	−0.364299	+	0.630985i	−0.988663	−	0.150148i	$-0.952025\pi$
$641$	−9.22332	+	15.9753i	−0.364299	+	0.630985i	0.624364	+	0.781133i	$0.285358\pi$
$642$		0			0
$643$	−19.3567			−0.763354			−0.381677	−	0.924296i	$-0.624653\pi$
$643$	−19.3567			−0.763354			−0.381677	+	0.924296i	$0.624653\pi$
$644$		0			0
$645$	3.60769	+	6.24871i	0.142053	+	0.246043i
$646$		0			0
$647$	−13.1644			−0.517547			−0.258773	−	0.965938i	$-0.583318\pi$
$647$	−13.1644			−0.517547			−0.258773	+	0.965938i	$0.583318\pi$
$648$		0			0
$649$	−9.64200			−0.378482
$650$		0			0
$651$	−10.3386	+	9.89418i	−0.405200	+	0.387784i
$652$		0			0
$653$	46.1500			1.80599			0.902995	−	0.429651i	$-0.141363\pi$
$653$	46.1500			1.80599			0.902995	+	0.429651i	$0.141363\pi$
$654$		0			0
$655$	−7.51047			−0.293459
$656$		0			0
$657$	−5.50655	−	9.53762i	−0.214831	−	0.372098i
$658$		0			0
$659$	−29.4011			−1.14530			−0.572652	−	0.819799i	$-0.694085\pi$
$659$	−29.4011			−1.14530			−0.572652	+	0.819799i	$0.694085\pi$
$660$		0			0
$661$	0.553421	−	0.958553i	0.0215256	−	0.0372834i	−0.855062	−	0.518526i	$-0.826481\pi$
$661$	0.553421	−	0.958553i	0.0215256	−	0.0372834i	0.876588	+	0.481242i	$0.159814\pi$
$662$		0			0
$663$	12.9772	+	22.4771i	0.503992	+	0.872939i
$664$		0			0
$665$	5.11424	+	8.85813i	0.198322	+	0.343503i
$666$		0			0
$667$	−4.89316			−0.189464
$668$		0			0
$669$	−11.7669	+	20.3809i	−0.454936	+	0.787973i
$670$		0			0
$671$	−0.383686	+	0.664564i	−0.0148120	+	0.0256552i
$672$		0			0
$673$	−19.0271	+	32.9559i	−0.733440	+	1.27036i	0.221964	+	0.975055i	$0.428753\pi$
$673$	−19.0271	+	32.9559i	−0.733440	+	1.27036i	−0.955404	+	0.295301i	$0.904580\pi$
$674$		0			0
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$		0			0
$677$	1.77434	−	3.07325i	0.0681935	−	0.118115i	−0.829913	−	0.557893i	$-0.811610\pi$
$677$	1.77434	−	3.07325i	0.0681935	−	0.118115i	0.898106	+	0.439779i	$0.144943\pi$
$678$		0			0
$679$	−10.5695	−	18.3070i	−0.405622	−	0.702558i
$680$		0			0
$681$	18.0903			0.693224
$682$		0			0
$683$	19.0744			0.729861			0.364930	−	0.931035i	$-0.381093\pi$
$683$	19.0744			0.729861			0.364930	+	0.931035i	$0.381093\pi$
$684$		0			0
$685$	5.74226	+	9.94589i	0.219401	+	0.380013i
$686$		0			0
$687$	4.70943	−	8.15697i	0.179676	−	0.311208i
$688$		0			0
$689$	34.4434	+	59.6578i	1.31219	+	2.27278i
$690$		0			0
$691$	−0.568899	+	0.985363i	−0.0216420	+	0.0374850i	−0.876644	−	0.481140i	$-0.840223\pi$
$691$	−0.568899	+	0.985363i	−0.0216420	+	0.0374850i	0.855002	+	0.518625i	$0.173556\pi$
$692$		0			0
$693$	2.75056	−	4.76410i	0.104485	−	0.180973i
$694$		0			0
$695$	−0.604714	+	1.04739i	−0.0229381	+	0.0397299i
$696$		0			0
$697$	−3.49793			−0.132493
$698$		0			0
$699$	−13.8579	−	24.0026i	−0.524155	−	0.907863i
$700$		0			0
$701$	8.72411	+	15.1106i	0.329505	+	0.570720i	0.982414	−	0.186717i	$-0.0597847\pi$
$701$	8.72411	+	15.1106i	0.329505	+	0.570720i	−0.652909	+	0.757437i	$0.726451\pi$
$702$		0			0
$703$	1.13457	−	1.96513i	0.0427910	−	0.0741162i
$704$		0			0
$705$	0.229753			0.00865299
$706$		0			0
$707$	−22.9765	−	39.7965i	−0.864122	−	1.49670i
$708$		0			0
$709$	−6.91027			−0.259521			−0.129760	−	0.991545i	$-0.541421\pi$
$709$	−6.91027			−0.259521			−0.129760	+	0.991545i	$0.541421\pi$
$710$		0			0
$711$	−15.2044			−0.570210
$712$		0			0
$713$	−40.9145	−	11.9318i	−1.53226	−	0.446851i
$714$		0			0
$715$	12.7987			0.478643
$716$		0			0
$717$	14.5555			0.543584
$718$		0			0
$719$	−2.10248	−	3.64161i	−0.0784095	−	0.135809i	0.824154	−	0.566365i	$-0.191651\pi$
$719$	−2.10248	−	3.64161i	−0.0784095	−	0.135809i	−0.902564	+	0.430556i	$0.858317\pi$
$720$		0			0
$721$	−23.7150			−0.883193
$722$		0			0
$723$	−6.30807	+	10.9259i	−0.234600	+	0.406339i
$724$		0			0
$725$	−0.319623	−	0.553604i	−0.0118705	−	0.0205603i
$726$		0			0
$727$	−6.46903	−	11.2047i	−0.239923	−	0.415559i	0.720769	−	0.693175i	$-0.243789\pi$
$727$	−6.46903	−	11.2047i	−0.239923	−	0.415559i	−0.960692	+	0.277616i	$0.910456\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−15.6589	+	27.1221i	−0.579167	+	1.00315i
$732$		0			0
$733$	−2.06124	+	3.57017i	−0.0761336	+	0.131867i	−0.901579	−	0.432615i	$-0.857591\pi$
$733$	−2.06124	+	3.57017i	−0.0761336	+	0.131867i	0.825445	+	0.564482i	$0.190924\pi$
$734$		0			0
$735$	−0.197086	+	0.341363i	−0.00726963	+	0.0125914i
$736$		0			0
$737$	−4.54300	−	7.86870i	−0.167343	−	0.289847i
$738$		0			0
$739$	−23.4314	+	40.5843i	−0.861937	+	1.49292i	0.00812049	+	0.999967i	$0.497415\pi$
$739$	−23.4314	+	40.5843i	−0.861937	+	1.49292i	−0.870057	+	0.492951i	$0.835918\pi$
$740$		0			0
$741$	11.8986	+	20.6089i	0.437105	+	0.757088i
$742$		0			0
$743$	0.598909			0.0219718			0.0109859	−	0.999940i	$-0.496503\pi$
$743$	0.598909			0.0219718			0.0109859	+	0.999940i	$0.496503\pi$
$744$		0			0
$745$	−5.00373			−0.183323
$746$		0			0
$747$	5.33027	+	9.23229i	0.195024	+	0.337792i
$748$		0			0
$749$	22.3812	−	38.7654i	0.817793	−	1.41646i
$750$		0			0
$751$	9.41450	+	16.3064i	0.343540	+	0.595029i	0.985087	−	0.172055i	$-0.0550406\pi$
$751$	9.41450	+	16.3064i	0.343540	+	0.595029i	−0.641547	+	0.767083i	$0.721707\pi$
$752$		0			0
$753$	−5.11488	+	8.85923i	−0.186396	+	0.322848i
$754$		0			0
$755$	0.532834	−	0.922895i	0.0193918	−	0.0335876i
$756$		0			0
$757$	14.4820	−	25.0836i	0.526358	−	0.911679i	−0.473170	−	0.880971i	$-0.656891\pi$
$757$	14.4820	−	25.0836i	0.526358	−	0.911679i	0.999528	−	0.0307078i	$-0.00977614\pi$
$758$		0			0
$759$	16.3835			0.594685
$760$		0			0
$761$	−19.9114	−	34.4876i	−0.721788	−	1.25017i	−0.960283	−	0.279029i	$-0.909987\pi$
$761$	−19.9114	−	34.4876i	−0.721788	−	1.25017i	0.238495	−	0.971144i	$-0.423346\pi$
$762$		0			0
$763$	−2.34399	−	4.05992i	−0.0848583	−	0.146979i
$764$		0			0
$765$	−2.17021	+	3.75892i	−0.0784642	+	0.135904i
$766$		0			0
$767$	−26.9375			−0.972657
$768$		0			0
$769$	−23.2024	−	40.1877i	−0.836700	−	1.44921i	−0.892639	−	0.450773i	$-0.851149\pi$
$769$	−23.2024	−	40.1877i	−0.836700	−	1.44921i	0.0559388	−	0.998434i	$-0.482185\pi$
$770$		0			0
$771$	−23.3876			−0.842283
$772$		0			0
$773$	39.2822			1.41288			0.706442	−	0.707771i	$-0.250299\pi$
$773$	39.2822			1.41288			0.706442	+	0.707771i	$0.250299\pi$
$774$		0			0
$775$	−1.32260	−	5.40839i	−0.0475093	−	0.194275i
$776$		0			0
$777$	−1.46547			−0.0525733
$778$		0			0
$779$	−3.20720			−0.114910
$780$		0			0
$781$	−11.8904	−	20.5948i	−0.425473	−	0.736941i
$782$		0			0
$783$	−0.639247			−0.0228448
$784$		0			0
$785$	11.2921	−	19.5585i	0.403033	−	0.698073i
$786$		0			0
$787$	−23.1899	−	40.1661i	−0.826630	−	1.43177i	−0.900667	−	0.434510i	$-0.856921\pi$
$787$	−23.1899	−	40.1661i	−0.826630	−	1.43177i	0.0740364	−	0.997256i	$-0.476412\pi$
$788$		0			0
$789$	6.93966	+	12.0198i	0.247058	+	0.427918i
$790$		0			0
$791$	−27.6350			−0.982586
$792$		0			0
$793$	−1.07193	+	1.85664i	−0.0380654	+	0.0659311i
$794$		0			0
$795$	−5.76008	+	9.97676i	−0.204289	+	0.353839i
$796$		0			0
$797$	−21.3226	+	36.9318i	−0.755285	+	1.30819i	0.189948	+	0.981794i	$0.439168\pi$
$797$	−21.3226	+	36.9318i	−0.755285	+	1.30819i	−0.945233	+	0.326398i	$0.894165\pi$
$798$		0			0
$799$	0.498613	+	0.863622i	0.0176396	+	0.0305528i
$800$		0			0
$801$	−1.75354	+	3.03722i	−0.0619582	+	0.107315i
$802$		0			0
$803$	−11.7860	−	20.4139i	−0.415919	−	0.720393i
$804$		0			0
$805$	19.6736			0.693404
$806$		0			0
$807$	2.27849			0.0802068
$808$		0			0
$809$	14.9382	+	25.8738i	0.525200	+	0.909674i	0.999569	+	0.0293475i	$0.00934293\pi$
$809$	14.9382	+	25.8738i	0.525200	+	0.909674i	−0.474369	+	0.880326i	$0.657324\pi$
$810$		0			0
$811$	−1.96823	+	3.40908i	−0.0691139	+	0.119709i	−0.898512	−	0.438950i	$-0.855351\pi$
$811$	−1.96823	+	3.40908i	−0.0691139	+	0.119709i	0.829398	+	0.558659i	$0.188684\pi$
$812$		0			0
$813$	−0.0676788	−	0.117223i	−0.00237360	−	0.00411119i
$814$		0			0
$815$	7.36591	−	12.7581i	0.258017	−	0.446898i
$816$		0			0
$817$	−14.3574	+	24.8678i	−0.502304	+	0.870015i
$818$		0			0
$819$	7.68442	−	13.3098i	0.268515	−	0.465082i
$820$		0			0
$821$	5.22635			0.182401			0.0912005	−	0.995833i	$-0.470930\pi$
$821$	5.22635			0.182401			0.0912005	+	0.995833i	$0.470930\pi$
$822$		0			0
$823$	3.98048	+	6.89439i	0.138751	+	0.240323i	0.927024	−	0.375002i	$-0.122358\pi$
$823$	3.98048	+	6.89439i	0.138751	+	0.240323i	−0.788273	+	0.615325i	$0.789025\pi$
$824$		0			0
$825$	1.07018	+	1.85361i	0.0372589	+	0.0645343i
$826$		0			0
$827$	−5.64345	+	9.77474i	−0.196242	+	0.339901i	−0.947307	−	0.320327i	$-0.896207\pi$
$827$	−5.64345	+	9.77474i	−0.196242	+	0.339901i	0.751065	+	0.660228i	$0.229540\pi$
$828$		0			0
$829$	−26.3767			−0.916101			−0.458050	−	0.888926i	$-0.651452\pi$
$829$	−26.3767			−0.916101			−0.458050	+	0.888926i	$0.651452\pi$
$830$		0			0
$831$	3.19990	+	5.54239i	0.111003	+	0.192263i
$832$		0			0
$833$	−1.71088			−0.0592783
$834$		0			0
$835$	−1.12004			−0.0387604
$836$		0			0
$837$	−5.34511	−	1.55879i	−0.184754	−	0.0538796i
$838$		0			0
$839$	16.1528			0.557658			0.278829	−	0.960341i	$-0.410054\pi$
$839$	16.1528			0.557658			0.278829	+	0.960341i	$0.410054\pi$
$840$		0			0
$841$	−28.5914			−0.985909
$842$		0			0
$843$	−5.82840	−	10.0951i	−0.200741	−	0.347693i
$844$		0			0
$845$	22.7565			0.782848
$846$		0			0
$847$	−8.24881	+	14.2874i	−0.283432	+	0.490919i
$848$		0			0
$849$	−6.32447	−	10.9543i	−0.217055	−	0.375951i
$850$		0			0
$851$	−2.18224	−	3.77976i	−0.0748063	−	0.129568i
$852$		0			0
$853$	−39.0740			−1.33787			−0.668935	−	0.743321i	$-0.733250\pi$
$853$	−39.0740			−1.33787			−0.668935	+	0.743321i	$0.733250\pi$
$854$		0			0
$855$	−1.98984	+	3.44650i	−0.0680510	+	0.117868i
$856$		0			0
$857$	−24.3649	+	42.2013i	−0.832291	+	1.44157i	0.0639268	+	0.997955i	$0.479638\pi$
$857$	−24.3649	+	42.2013i	−0.832291	+	1.44157i	−0.896217	+	0.443615i	$0.853696\pi$
$858$		0			0
$859$	17.4217	−	30.1753i	0.594422	−	1.02957i	−0.399206	−	0.916861i	$-0.630714\pi$
$859$	17.4217	−	30.1753i	0.594422	−	1.02957i	0.993628	−	0.112708i	$-0.0359523\pi$
$860$		0			0
$861$	1.03565	+	1.79379i	0.0352948	+	0.0611323i
$862$		0			0
$863$	−8.65270	+	14.9869i	−0.294541	+	0.510161i	−0.974878	−	0.222739i	$-0.928500\pi$
$863$	−8.65270	+	14.9869i	−0.294541	+	0.510161i	0.680337	+	0.732900i	$0.261834\pi$
$864$		0			0
$865$	−5.65128	−	9.78830i	−0.192149	−	0.332812i
$866$		0			0
$867$	−1.83931			−0.0624664
$868$		0			0
$869$	−32.5430			−1.10394
$870$		0			0
$871$	−12.6921	−	21.9833i	−0.430055	−	0.744877i
$872$		0			0
$873$	4.11237	−	7.12284i	0.139183	−	0.241072i
$874$		0			0
$875$	1.28509	+	2.22584i	0.0434440	+	0.0752472i
$876$		0			0
$877$	−14.4045	+	24.9493i	−0.486405	+	0.842478i	−0.999878	−	0.0156276i	$-0.995025\pi$
$877$	−14.4045	+	24.9493i	−0.486405	+	0.842478i	0.513473	+	0.858106i	$0.328359\pi$
$878$		0			0
$879$	−0.890918	+	1.54312i	−0.0300499	+	0.0520480i
$880$		0			0
$881$	6.94403	−	12.0274i	0.233950	−	0.405214i	−0.725017	−	0.688731i	$-0.758168\pi$
$881$	6.94403	−	12.0274i	0.233950	−	0.405214i	0.958967	+	0.283517i	$0.0915014\pi$
$882$		0			0
$883$	−43.0010			−1.44710			−0.723549	−	0.690273i	$-0.757490\pi$
$883$	−43.0010			−1.44710			−0.723549	+	0.690273i	$0.757490\pi$
$884$		0			0
$885$	−2.25242	−	3.90131i	−0.0757144	−	0.131141i
$886$		0			0
$887$	8.64351	+	14.9710i	0.290221	+	0.502677i	0.973862	−	0.227141i	$-0.0729380\pi$
$887$	8.64351	+	14.9710i	0.290221	+	0.502677i	−0.683641	+	0.729818i	$0.739605\pi$
$888$		0			0
$889$	−28.7030	+	49.7151i	−0.962669	+	1.66739i
$890$		0			0
$891$	2.14036			0.0717048
$892$		0			0
$893$	0.457171	+	0.791843i	0.0152986	+	0.0264980i
$894$		0			0
$895$	−6.51143			−0.217653
$896$		0			0
$897$	45.7718			1.52828
$898$		0			0
$899$	3.41684	+	0.996450i	0.113958	+	0.0332335i
$900$		0			0
$901$	−50.0025			−1.66582
$902$		0			0
$903$	18.5449			0.617134
$904$		0			0
$905$	2.57784	+	4.46495i	0.0856904	+	0.148420i
$906$		0			0
$907$	28.8188			0.956912			0.478456	−	0.878112i	$-0.341197\pi$
$907$	28.8188			0.956912			0.478456	+	0.878112i	$0.341197\pi$
$908$		0			0
$909$	8.93966	−	15.4839i	0.296510	−	0.513570i
$910$		0			0
$911$	11.1585	+	19.3271i	0.369697	+	0.640335i	0.989518	−	0.144409i	$-0.0461280\pi$
$911$	11.1585	+	19.3271i	0.369697	+	0.640335i	−0.619821	+	0.784744i	$0.712795\pi$
$912$		0			0
$913$	11.4087	+	19.7604i	0.377573	+	0.653975i
$914$		0			0
$915$	−0.358525			−0.0118525
$916$		0			0
$917$	−9.65164	+	16.7171i	−0.318725	+	0.552048i
$918$		0			0
$919$	13.8462	−	23.9824i	0.456745	−	0.791105i	−0.542042	−	0.840351i	$-0.682349\pi$
$919$	13.8462	−	23.9824i	0.456745	−	0.791105i	0.998787	+	0.0492464i	$0.0156819\pi$
$920$		0			0
$921$	−7.91061	+	13.7016i	−0.260663	+	0.451482i
$922$		0			0
$923$	−33.2191	−	57.5372i	−1.09342	−	1.89386i
$924$		0			0
$925$	0.285090	−	0.493791i	0.00937371	−	0.0162357i
$926$		0			0
$927$	−4.61349	−	7.99080i	−0.151527	−	0.262452i
$928$		0			0
$929$	−12.6599			−0.415357			−0.207679	−	0.978197i	$-0.566591\pi$
$929$	−12.6599			−0.415357			−0.207679	+	0.978197i	$0.566591\pi$
$930$		0			0
$931$	−1.56868			−0.0514113
$932$		0			0
$933$	−4.50953	−	7.81073i	−0.147635	−	0.255712i
$934$		0			0
$935$	−4.64504	+	8.04545i	−0.151909	+	0.263114i
$936$		0			0
$937$	−5.72996	−	9.92458i	−0.187190	−	0.324222i	0.757123	−	0.653273i	$-0.226605\pi$
$937$	−5.72996	−	9.92458i	−0.187190	−	0.324222i	−0.944312	+	0.329051i	$0.893271\pi$
$938$		0			0
$939$	−0.146429	+	0.253622i	−0.00477852	+	0.00827664i
$940$		0			0
$941$	−5.52346	+	9.56692i	−0.180060	+	0.311873i	−0.941901	−	0.335892i	$-0.890962\pi$
$941$	−5.52346	+	9.56692i	−0.180060	+	0.311873i	0.761841	+	0.647764i	$0.224296\pi$
$942$		0			0
$943$	−3.08439	+	5.34232i	−0.100441	+	0.173970i
$944$		0			0
$945$	2.57018			0.0836080
$946$		0			0
$947$	−17.8770	−	30.9638i	−0.580924	−	1.00619i	−0.995370	−	0.0961159i	$-0.969358\pi$
$947$	−17.8770	−	30.9638i	−0.580924	−	1.00619i	0.414446	−	0.910074i	$-0.363975\pi$
$948$		0			0
$949$	−32.9274	−	57.0319i	−1.06887	−	1.85133i
$950$		0			0
$951$	5.61722	−	9.72931i	0.182151	−	0.315495i
$952$		0			0
$953$	−30.2393			−0.979549			−0.489774	−	0.871849i	$-0.662921\pi$
$953$	−30.2393			−0.979549			−0.489774	+	0.871849i	$0.662921\pi$
$954$		0			0
$955$	−7.22007	−	12.5055i	−0.233636	−	0.404669i
$956$		0			0
$957$	−1.36822			−0.0442282
$958$		0			0
$959$	29.5173			0.953163
$960$		0			0
$961$	26.1404	+	16.6638i	0.843237	+	0.537541i
$962$		0			0
$963$	17.4161			0.561225
$964$		0			0
$965$	−19.5164			−0.628256
$966$		0			0
$967$	9.48622	+	16.4306i	0.305056	+	0.528373i	0.977274	−	0.211981i	$-0.0679914\pi$
$967$	9.48622	+	16.4306i	0.305056	+	0.528373i	−0.672218	+	0.740354i	$0.734658\pi$
$968$		0			0
$969$	−17.2735			−0.554904
$970$		0			0
$971$	−1.41529	+	2.45135i	−0.0454188	+	0.0786676i	−0.887841	−	0.460150i	$-0.847796\pi$
$971$	−1.41529	+	2.45135i	−0.0454188	+	0.0786676i	0.842422	+	0.538818i	$0.181129\pi$
$972$		0			0
$973$	1.55422	+	2.69199i	0.0498261	+	0.0863014i
$974$		0			0
$975$	2.98984	+	5.17855i	0.0957514	+	0.165846i
$976$		0			0
$977$	8.79548			0.281392			0.140696	−	0.990053i	$-0.455066\pi$
$977$	8.79548			0.281392			0.140696	+	0.990053i	$0.455066\pi$
$978$		0			0
$979$	−3.75320	+	6.50074i	−0.119953	+	0.207765i
$980$		0			0
$981$	0.911996	−	1.57962i	0.0291178	−	0.0504335i
$982$		0			0
$983$	−25.6214	+	44.3776i	−0.817196	+	1.41543i	0.0905441	+	0.995892i	$0.471139\pi$
$983$	−25.6214	+	44.3776i	−0.817196	+	1.41543i	−0.907740	+	0.419533i	$0.862194\pi$
$984$		0			0
$985$	−7.11237	−	12.3190i	−0.226619	−	0.392516i
$986$		0			0
$987$	0.295253	−	0.511393i	0.00939801	−	0.0162778i
$988$		0			0
$989$	27.6153	+	47.8312i	0.878117	+	1.52094i
$990$		0			0
$991$	10.9519			0.347898			0.173949	−	0.984755i	$-0.444347\pi$
$991$	10.9519			0.347898			0.173949	+	0.984755i	$0.444347\pi$
$992$		0			0
$993$	−33.1757			−1.05280
$994$		0			0
$995$	9.67489	+	16.7574i	0.306715	+	0.531246i
$996$		0			0
$997$	5.66973	−	9.82027i	0.179562	−	0.311011i	−0.762168	−	0.647379i	$-0.775865\pi$
$997$	5.66973	−	9.82027i	0.179562	−	0.311011i	0.941731	+	0.336368i	$0.109199\pi$
$998$		0			0
$999$	−0.285090	−	0.493791i	−0.00901986	−	0.0156229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1860.2.q.h.1141.3	✓	8
31.5	even	3	inner	1860.2.q.h.1741.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.2.q.h.1141.3	✓	8	1.1	even	1	trivial
1860.2.q.h.1741.3	yes	8	31.5	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1860.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.28509 + 2.22584i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.07018 + 1.85361i) q^{11} +(-2.98984 + 5.17855i) q^{13} -1.00000 q^{15} +(-2.17021 - 3.75892i) q^{17} +(-1.98984 - 3.44650i) q^{19} +(-1.28509 + 2.22584i) q^{21} -7.65457 q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +0.639247 q^{29} +(5.34511 + 1.55879i) q^{31} -2.14036 q^{33} -2.57018 q^{35} +(0.285090 + 0.493791i) q^{37} -5.97967 q^{39} +(0.402947 - 0.697925i) q^{41} +(-3.60769 - 6.24871i) q^{43} +(-0.500000 - 0.866025i) q^{45} -0.229753 q^{47} +(0.197086 - 0.341363i) q^{49} +(2.17021 - 3.75892i) q^{51} +(5.76008 - 9.97676i) q^{53} +(-1.07018 - 1.85361i) q^{55} +(1.98984 - 3.44650i) q^{57} +(2.25242 + 3.90131i) q^{59} +0.358525 q^{61} -2.57018 q^{63} +(-2.98984 - 5.17855i) q^{65} +(-2.12254 + 3.67634i) q^{67} +(-3.82728 - 6.62905i) q^{69} +(-5.55534 + 9.62213i) q^{71} +(-5.50655 + 9.53762i) q^{73} +(0.500000 - 0.866025i) q^{75} -5.50111 q^{77} +(7.60221 + 13.1674i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.33027 - 9.23229i) q^{83} +4.34043 q^{85} +(0.319623 + 0.553604i) q^{87} +3.50708 q^{89} -15.3688 q^{91} +(1.32260 + 5.40839i) q^{93} +3.97967 q^{95} -8.22475 q^{97} +(-1.07018 - 1.85361i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{5} + 6 q^{7} - 4 q^{9} - q^{13} - 8 q^{15} - 7 q^{17} + 7 q^{19} - 6 q^{21} + 10 q^{23} - 4 q^{25} - 8 q^{27} - 20 q^{29} + 7 q^{31} - 12 q^{35} - 2 q^{37} - 2 q^{39} - 3 q^{41} - 4 q^{43}+ \cdots + 14 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^5 + 6 * q^7 - 4 * q^9 - q^13 - 8 * q^15 - 7 * q^17 + 7 * q^19 - 6 * q^21 + 10 * q^23 - 4 * q^25 - 8 * q^27 - 20 * q^29 + 7 * q^31 - 12 * q^35 - 2 * q^37 - 2 * q^39 - 3 * q^41 - 4 * q^43 - 4 * q^45 - 14 * q^47 + 6 * q^49 + 7 * q^51 + 11 * q^53 - 7 * q^57 + 6 * q^59 + 12 * q^61 - 12 * q^63 - q^65 + 5 * q^69 - 28 * q^71 - 13 * q^73 + 4 * q^75 - 52 * q^77 - 2 * q^79 - 4 * q^81 - q^83 + 14 * q^85 - 10 * q^87 + 20 * q^89 + 6 * q^91 - 10 * q^93 - 14 * q^95 + 14 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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